## Topic outline

• ### General

Probability And Random Variables

 Instructor: Elif Uysal

• ### Topic 1

Introduction to probability theory; Review of set theory
• ### Topic 2

Probability Spaces; Axioms and properties or probability
• ### Topic 3

Discrete and Continuous Probability Laws, Conditional Probability
• ### Topic 4

Total Probability Theorem, Bayes's Rule
• ### Topic 5

Independence, Conditional Independence
• ### Topic 6

Independent Trials, Counting
• ### Topic 7

Discrete Random Variables
• ### Topic 8

Expectation and Variance
• ### Topic 9

Properties of Expectation and Variance, Joint PMFs

• ### Topic 10

Conditional PMFs
• ### Topic 11

Conditioning one Random Variable on another; conditional expectation

• ### Topic 12

Iterated Expectation; Independence of a random variable from an event

• ### Topic 13

Independence of Random Variables

• ### Topic 14

Continuous Random Variables

• ### Topic 15

Expectation and the Cumulative Distribution Function

• ### Topic 16

The Gaussian CDF

• ### Topic 17

Conditional PDFs, Joint PDFs

• ### Topic 18

Conditioning one random variable on another

• ### Topic 19

Independence, Continuous Bayes's Rule; Derived Distributions

• ### Topic 20

Derived Distributions

• ### Topic 21

Functions of Two Random Variables; Correlation and Covariance

• ### Topic 22

Applications of Covariance

• ### Topic 23

Transforms (Moment Generating Functions)

• ### Topic 24

Markov and Chebychev Inequalities, Convergence In Probability

• ### Topic 25

The Weak Law of Large Numbers

• ### Topic 26

The Central Limit Theorem

• ### Topic 27

The Bernoulli Process

• ### Topic 28

The Poisson Process